A simplified model to calculate the surface-to-volume atomic ratio dependent cohesive energy of nanocrystals

A simplified model for the surface-to-volume atomic ratio dependent cohesive energy of nanocrystals is obtained in this letter. On the basis of the model, we predict that the cohesive energy can not only decrease but also increase with the increasing surface-to-volume atomic ratio under different conditions. The model predictions are found to be in agreement with the experimental values of Mo and W nanoparticles. The conditions on the cohesive energy of an embedded nanocrystal increasing or decreasing with the increasing surface-to-volume atomic ratio are discussed. The relations between the cohesive energy of nanoparticles, nanowires and nanofilms, and the shape effect on nanoparticles are also discussed. Since the cohesive energy is regarded as being directly related to the nature of the thermal stability of nanocrystals, the relationship to the phenomenon of melting and superheating given by our cohesive energy model seems sensible.